The Hubble Space Telescope has excellent resolving power because there is no atmospheric distortion of the light. The Hubble deep field camera uses the 2.4 m diameter mirror to collect light from distant galaxies that formed very early in the history of the universe. How far apart can two galaxies be from each other if they are 11 billion light-years away from Earth and are barely resolved by the Hubble Telescope using visible light with a wavelength of 470 nm?
Please, point it at the Moon where we left all the spack junk when we landed, i would like to see the latter?
January 1st, 2010 at 5:57 pm
Using the equation:
R = λ / D
Where R is the angle between the two objects radians, λ is the wavelength of light, and D is the diameter of the objective we get:
R = 470e-9 m / 2.4m = 1.958e-7
Given the angle R and the radius r = 11 billion light years
We calculate the arc length (s) using the equation:
R = s/r
s = R*r = 11e9 light years * 1.958e-7 = 2153.8 light years.
Note: the actual length between the two galaxies is a straight light rather than an arc, but the angle R is small enough for the difference to be insignificant.
The actual length can be calculated using the fact that the distance between the stars and the Earth forms an isosceles triangle:
d = 2*r*sin(0.5*R) = 2*11e9 light years * sin (0.5*1.958e-7)
= 2153.8 light years
Take the answer to 2 significant figures: 2200 light years.
Answer:
The two galaxies are located 2200 light years apart.
References :
http://en.wikipedia.org/wiki/Angular_resolution#Single_telescope_case
http://www.themathpage.com/aTrig/arc-length.htm
http://mathworld.wolfram.com/IsoscelesTriangle.html
January 1st, 2010 at 6:32 pm
L (distance) = sin θ * 7×10^9 = λ/D* 11×10^9ly = 2154.167ly
2154.167*1.22 = 2628.08 ly
answer: 2628.08ly
References :
January 1st, 2010 at 6:40 pm
Please, point it at the Moon where we left all the spack junk when we landed, i would like to see the latter?
References :